Single photon emission computed tomography (SPECT) has become an important diagnostic tool in cardiovascular nuclear medicine. Most cardiac SPECT procedures are performed using a large field-of-view rotating gamma camera. For a small organ like the heart, a converging geometry can be utilized to improve the geometric efficiency and resolution of SPECT images. Combining converging collimation with multi- detector SPECT system offers an additional advantage of simultaneous transmission-emission tomography capability that can attenuation correct cardiac images without increasing patient imaging time; however, through this research we intend to demonstrate that attenuation-corrected cardiac images may be possible without having to acquire transmission data. The methods developed will improve spatial and contrast resolution of cardiac images as well as improve quantification of radiopharmaceutical uptake which is important for better diagnosis of coronary artery disease and more accurate evaluation of viable myocardial tissue. Over the duration of this study we have participate in significant advancements in quantitative cardiac SPECT, particularly in the correction for physical factors of attenuation, geometric point response, and scatter. The work we are proposing will improve upon past work of developing methods to better quantify myocardial perfusion and extend to evaluating cardiac viability using FDG and gated 3D deformation models of the heart. This study will apply converging collimation to cardiac imaging using multi-detector SPECT systems and will develop new algorithms that reconstruct three-dimensional images of the heart without artifacts, from projects obtained using converging collimators with and without acquisition of a transmission study. The proposed research will result in the following: (1) New algorithms for reconstructing data from covering geometries. (2) Improved, truncated transmission reconstructions. (3) Reconstruction of attenuation-, and collimator geometric response-, and scatter-corrected cardiac images within clinically acceptable processing times. (4) A 3D scatter and geometric response correction technique using a ray-tracing projector- back-projector. (5) Attenuation-correction techniques that do not require a transmission study. (6) A 3D deformation model of the beating myocardium using mechanical properties of the myocardium. (7) Evaluation of conventional imaging techniques with proposed new imaging techniques using human observer experiments and a determination of the correlation of the ROC results with that of the Hotelling ideal observer.